Quantized fault‐tolerant consensus for multiple Lagrangian systems subject to switching networks

Abstract This article is concerned with the quantized fault‐tolerant control (FTC) for consensus of multiple Lagrangian systems subject to stochastically switching networks, actuator and sensor faults. First of all, a reliable quantized FTC algorithm is developed under Markov jump networks (MJNs), where the communication signal is first quantized before transmitted to develop controllers, and the communication networks are stochastically switching with the sojourn time belonging to an exponential distribution. Then, to handle the FTC problem in the presence of unknown control directions, the Nussbaum function is introduced to further improve the control reliability. Furthermore, the FTC case involving semi‐Markov jump networks (S‐MJNs) and time‐varying communication delays is considered, where the negative constraints of time delays can be effectively attenuated with the sojourn time following a Weibull distribution. Meanwhile, several sufficient criteria on the consensus analysis and algorithms synthesis are established by means of the Lyapunov–Krasovskii stability method. Finally, numerous illustrative examples are elaborated on for demonstrating the feasibility of the derived results.